PayPal is a popular online payment processing system which is actually owned by eBay. You create an account which is used to store your electronic funds. You can make payments or send and receive money using your account.
For online shoppers the system will allow you to use your PayPal balance to make payments, your account can then default to a credit card to pay the balance.
When using the online shopping carts you will see a button that will start your PayPal transaction, this usually happens instantly after you have logged in. For more information on how the system works visit the Paypal website.